This thesis concerns a technical hurdle that must be overcome in relation to air-breathing propulsion technologies for future space access vehicles--it discusses the flow starting process in supersonic and hypersonic air-inlets. A study is conducted, with the aid of numerical simulations, based on an inviscid model of a thermally perfect gas.Effects of boundary-imposed temporal and spatial gradients on the inlet starting phenomenon are documented for the first time. It is shown that purely accelerative starting is generally not possible, for inlets of any positive contraction, unless thousands of g 's of acceleration are imposed. It is proposed that removal of frangible structures, such as fast rupturing diaphragms, be used to impose sufficiently high spatial gradients, as necessary to permit starting beyond Kantrowitz' limit. It is shown that, for a perforated diffuser, starting takes place if a sonic line, at the leading edge of a slit, occurs at an area ratio equal to, or higher than, that corresponding to Kantrowitz' limit.